diff options
author | Måns Rullgård <mans@mansr.com> | 2010-07-01 23:21:39 +0000 |
---|---|---|
committer | Måns Rullgård <mans@mansr.com> | 2010-07-01 23:21:39 +0000 |
commit | bf7ba153729e2ea645cd6cc1150514137037923c (patch) | |
tree | 5d3feab4068e937b46164124edb1168a8a657ba1 /libavcodec/ppc | |
parent | 135448fa1ac2622250b595c5135ddc573fcbd7b5 (diff) | |
download | ffmpeg-bf7ba153729e2ea645cd6cc1150514137037923c.tar.gz |
PPC: Altivec split-radix FFT
1.8x faster than altivec radix-2 on a G4
8% faster vorbis decoding
Patch (mostly) by Loren Merritt
Originally committed as revision 23956 to svn://svn.ffmpeg.org/ffmpeg/trunk
Diffstat (limited to 'libavcodec/ppc')
-rw-r--r-- | libavcodec/ppc/Makefile | 6 | ||||
-rw-r--r-- | libavcodec/ppc/fft_altivec.c | 152 | ||||
-rw-r--r-- | libavcodec/ppc/fft_altivec_s.S | 335 | ||||
-rw-r--r-- | libavcodec/ppc/types_altivec.h | 1 |
4 files changed, 396 insertions, 98 deletions
diff --git a/libavcodec/ppc/Makefile b/libavcodec/ppc/Makefile index 3bbd6c3630..175b1093b0 100644 --- a/libavcodec/ppc/Makefile +++ b/libavcodec/ppc/Makefile @@ -13,10 +13,14 @@ ALTIVEC-OBJS-$(CONFIG_MP3FLOAT_DECODER) += ppc/mpegaudiodec_altivec.o ALTIVEC-OBJS-$(CONFIG_MP3ON4FLOAT_DECODER) += ppc/mpegaudiodec_altivec.o ALTIVEC-OBJS-$(CONFIG_MP3ADUFLOAT_DECODER) += ppc/mpegaudiodec_altivec.o +FFT-OBJS-$(HAVE_GNU_AS) += ppc/fft_altivec_s.o \ + +ALTIVEC-OBJS-$(CONFIG_FFT) += ppc/fft_altivec.o \ + $(FFT-OBJS-yes) + OBJS-$(HAVE_ALTIVEC) += ppc/check_altivec.o \ ppc/dsputil_altivec.o \ ppc/fdct_altivec.o \ - ppc/fft_altivec.o \ ppc/float_altivec.o \ ppc/gmc_altivec.o \ ppc/idct_altivec.o \ diff --git a/libavcodec/ppc/fft_altivec.c b/libavcodec/ppc/fft_altivec.c index 5ef3bd3559..3f622c3aba 100644 --- a/libavcodec/ppc/fft_altivec.c +++ b/libavcodec/ppc/fft_altivec.c @@ -1,8 +1,7 @@ /* * FFT/IFFT transforms * AltiVec-enabled - * Copyright (c) 2003 Romain Dolbeau <romain@dolbeau.org> - * Based on code Copyright (c) 2002 Fabrice Bellard + * Copyright (c) 2009 Loren Merritt * * This file is part of FFmpeg. * @@ -22,7 +21,8 @@ */ #include "libavcodec/fft.h" #include "util_altivec.h" -#include "dsputil_altivec.h" +#include "types_altivec.h" +#include "regs.h" /** * Do a complex FFT with the parameters defined in ff_fft_init(). The @@ -31,107 +31,65 @@ * AltiVec-enabled * This code assumes that the 'z' pointer is 16 bytes-aligned * It also assumes all FFTComplex are 8 bytes-aligned pair of float - * The code is exactly the same as the SSE version, except - * that successive MUL + ADD/SUB have been merged into - * fused multiply-add ('vec_madd' in altivec) */ -static void ff_fft_calc_altivec(FFTContext *s, FFTComplex *z) -{ - register const vector float vczero = (const vector float)vec_splat_u32(0.); - - int ln = s->nbits; - int j, np, np2; - int nblocks, nloops; - register FFTComplex *p, *q; - FFTComplex *cptr, *cptr1; - int k; - - np = 1 << ln; - - { - vector float *r, a, b, a1, c1, c2; - - r = (vector float *)&z[0]; - - c1 = vcii(p,p,n,n); - - if (s->inverse) { - c2 = vcii(p,p,n,p); - } else { - c2 = vcii(p,p,p,n); - } - - j = (np >> 2); - do { - a = vec_ld(0, r); - a1 = vec_ld(sizeof(vector float), r); - - b = vec_perm(a,a,vcprmle(1,0,3,2)); - a = vec_madd(a,c1,b); - /* do the pass 0 butterfly */ - - b = vec_perm(a1,a1,vcprmle(1,0,3,2)); - b = vec_madd(a1,c1,b); - /* do the pass 0 butterfly */ - /* multiply third by -i */ - b = vec_perm(b,b,vcprmle(2,3,1,0)); +// Pointers to functions. Not using function pointer syntax, because +// that involves an extra level of indirection on some PPC ABIs. +extern void *ff_fft_dispatch_altivec[2][15]; - /* do the pass 1 butterfly */ - vec_st(vec_madd(b,c2,a), 0, r); - vec_st(vec_nmsub(b,c2,a), sizeof(vector float), r); - - r += 2; - } while (--j != 0); +// Convert from simd order to C order. +static void swizzle(vec_f *z, int n) +{ + int i; + n >>= 1; + for (i = 0; i < n; i += 2) { + vec_f re = z[i]; + vec_f im = z[i+1]; + z[i] = vec_mergeh(re, im); + z[i+1] = vec_mergel(re, im); } - /* pass 2 .. ln-1 */ - - nblocks = np >> 3; - nloops = 1 << 2; - np2 = np >> 1; - - cptr1 = s->exptab1; - do { - p = z; - q = z + nloops; - j = nblocks; - do { - cptr = cptr1; - k = nloops >> 1; - do { - vector float a,b,c,t1; - - a = vec_ld(0, (float*)p); - b = vec_ld(0, (float*)q); - - /* complex mul */ - c = vec_ld(0, (float*)cptr); - /* cre*re cim*re */ - t1 = vec_madd(c, vec_perm(b,b,vcprmle(2,2,0,0)),vczero); - c = vec_ld(sizeof(vector float), (float*)cptr); - /* -cim*im cre*im */ - b = vec_madd(c, vec_perm(b,b,vcprmle(3,3,1,1)),t1); - - /* butterfly */ - vec_st(vec_add(a,b), 0, (float*)p); - vec_st(vec_sub(a,b), 0, (float*)q); - - p += 2; - q += 2; - cptr += 4; - } while (--k); +} - p += nloops; - q += nloops; - } while (--j); - cptr1 += nloops * 2; - nblocks = nblocks >> 1; - nloops = nloops << 1; - } while (nblocks != 0); +static void ff_fft_calc_altivec(FFTContext *s, FFTComplex *z) +{ + register vec_f v14 __asm__("v14") = {0,0,0,0}; + register vec_f v15 __asm__("v15") = *(const vec_f*)ff_cos_16; + register vec_f v16 __asm__("v16") = {0, 0.38268343, M_SQRT1_2, 0.92387953}; + register vec_f v17 __asm__("v17") = {-M_SQRT1_2, M_SQRT1_2, M_SQRT1_2,-M_SQRT1_2}; + register vec_f v18 __asm__("v18") = { M_SQRT1_2, M_SQRT1_2, M_SQRT1_2, M_SQRT1_2}; + register vec_u8 v19 __asm__("v19") = vcprm(s0,3,2,1); + register vec_u8 v20 __asm__("v20") = vcprm(0,1,s2,s1); + register vec_u8 v21 __asm__("v21") = vcprm(2,3,s0,s3); + register vec_u8 v22 __asm__("v22") = vcprm(2,s3,3,s2); + register vec_u8 v23 __asm__("v23") = vcprm(0,1,s0,s1); + register vec_u8 v24 __asm__("v24") = vcprm(2,3,s2,s3); + register vec_u8 v25 __asm__("v25") = vcprm(2,3,0,1); + register vec_u8 v26 __asm__("v26") = vcprm(1,2,s3,s0); + register vec_u8 v27 __asm__("v27") = vcprm(0,3,s2,s1); + register vec_u8 v28 __asm__("v28") = vcprm(0,2,s1,s3); + register vec_u8 v29 __asm__("v29") = vcprm(1,3,s0,s2); + register FFTSample *const*cos_tabs __asm__("r12") = ff_cos_tabs; + register FFTComplex *zarg __asm__("r3") = z; + __asm__( + "mtctr %0 \n" + "li "r(9)", 16 \n" + "subi "r(1)","r(1) ",%1 \n" + "bctrl \n" + "addi "r(1)","r(1) ",%1 \n" + ::"r"(ff_fft_dispatch_altivec[1][s->nbits-2]), "i"(12*sizeof(void*)), + "r"(zarg), "r"(cos_tabs), + "v"(v14),"v"(v15),"v"(v16),"v"(v17),"v"(v18),"v"(v19),"v"(v20),"v"(v21), + "v"(v22),"v"(v23),"v"(v24),"v"(v25),"v"(v26),"v"(v27),"v"(v28),"v"(v29) + : "lr","ctr","r0","r4","r5","r6","r7","r8","r9","r10","r11", + "v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11","v12","v13" + ); + if (s->nbits <= 4) + swizzle((vec_f*)z, 1<<s->nbits); } av_cold void ff_fft_init_altivec(FFTContext *s) { - s->fft_calc = ff_fft_calc_altivec; - s->split_radix = 0; + if (HAVE_GNU_AS) + s->fft_calc = ff_fft_calc_altivec; + s->split_radix = 1; } diff --git a/libavcodec/ppc/fft_altivec_s.S b/libavcodec/ppc/fft_altivec_s.S new file mode 100644 index 0000000000..ed7b045e40 --- /dev/null +++ b/libavcodec/ppc/fft_altivec_s.S @@ -0,0 +1,335 @@ +/* + * FFT transform with Altivec optimizations + * Copyright (c) 2009 Loren Merritt + * + * This file is part of FFmpeg. + * + * FFmpeg is free software; you can redistribute it and/or + * modify it under the terms of the GNU Lesser General Public + * License as published by the Free Software Foundation; either + * version 2.1 of the License, or (at your option) any later version. + * + * FFmpeg is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public + * License along with FFmpeg; if not, write to the Free Software + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA + */ + +/* + * These functions are not individually interchangeable with the C versions. + * While C takes arrays of FFTComplex, Altivec leaves intermediate results + * in blocks as convenient to the vector size. + * i.e. {4x real, 4x imaginary, 4x real, ...} + * + * I ignore standard calling convention. + * Instead, the following registers are treated as global constants: + * v14: zero + * v15..v18: cosines + * v19..v29: permutations + * r9: 16 + * r12: ff_cos_tabs + * and the rest are free for local use. + */ + +#include "config.h" +#include "asm.S" + +.text + +/* Apple gas doesn't support this shorthand */ +.macro mtctr rx + mtspr 9, \rx +.endm + +.macro addi2 ra, imm // add 32-bit immediate +.if \imm & 0xffff + addi \ra, \ra, \imm@l +.endif +.if (\imm+0x8000)>>16 + addis \ra, \ra, \imm@ha +.endif +.endm + +#if ARCH_PPC64 +#define PTR .quad +.macro LOAD_PTR ra, rbase, offset + ld \ra,(\offset)*8(\rbase) +.endm +.macro STORE_PTR ra, rbase, offset + std \ra,(\offset)*8(\rbase) +.endm +#else +#define PTR .int +.macro LOAD_PTR ra, rbase, offset + lwz \ra,(\offset)*4(\rbase) +.endm +.macro STORE_PTR ra, rbase, offset + stw \ra,(\offset)*4(\rbase) +.endm +#endif + +.macro FFT4 a0, a1, a2, a3 // in:0-1 out:2-3 + vperm \a2,\a0,\a1,v20 // vcprm(0,1,s2,s1) // {r0,i0,r3,i2} + vperm \a3,\a0,\a1,v21 // vcprm(2,3,s0,s3) // {r1,i1,r2,i3} + vaddfp \a0,\a2,\a3 // {t1,t2,t6,t5} + vsubfp \a1,\a2,\a3 // {t3,t4,t8,t7} + vmrghw \a2,\a0,\a1 // vcprm(0,s0,1,s1) // {t1,t3,t2,t4} + vperm \a3,\a0,\a1,v22 // vcprm(2,s3,3,s2) // {t6,t7,t5,t8} + vaddfp \a0,\a2,\a3 // {r0,r1,i0,i1} + vsubfp \a1,\a2,\a3 // {r2,r3,i2,i3} + vperm \a2,\a0,\a1,v23 // vcprm(0,1,s0,s1) // {r0,r1,r2,r3} + vperm \a3,\a0,\a1,v24 // vcprm(2,3,s2,s3) // {i0,i1,i2,i3} +.endm + +.macro FFT4x2 a0, a1, b0, b1, a2, a3, b2, b3 + vperm \a2,\a0,\a1,v20 // vcprm(0,1,s2,s1) // {r0,i0,r3,i2} + vperm \a3,\a0,\a1,v21 // vcprm(2,3,s0,s3) // {r1,i1,r2,i3} + vperm \b2,\b0,\b1,v20 + vperm \b3,\b0,\b1,v21 + vaddfp \a0,\a2,\a3 // {t1,t2,t6,t5} + vsubfp \a1,\a2,\a3 // {t3,t4,t8,t7} + vaddfp \b0,\b2,\b3 + vsubfp \b1,\b2,\b3 + vmrghw \a2,\a0,\a1 // vcprm(0,s0,1,s1) // {t1,t3,t2,t4} + vperm \a3,\a0,\a1,v22 // vcprm(2,s3,3,s2) // {t6,t7,t5,t8} + vmrghw \b2,\b0,\b1 + vperm \b3,\b0,\b1,v22 + vaddfp \a0,\a2,\a3 // {r0,r1,i0,i1} + vsubfp \a1,\a2,\a3 // {r2,r3,i2,i3} + vaddfp \b0,\b2,\b3 + vsubfp \b1,\b2,\b3 + vperm \a2,\a0,\a1,v23 // vcprm(0,1,s0,s1) // {r0,r1,r2,r3} + vperm \a3,\a0,\a1,v24 // vcprm(2,3,s2,s3) // {i0,i1,i2,i3} + vperm \b2,\b0,\b1,v23 + vperm \b3,\b0,\b1,v24 +.endm + +.macro FFT8 a0, a1, b0, b1, a2, a3, b2, b3, b4 // in,out:a0-b1 + vmrghw \b2,\b0,\b1 // vcprm(0,s0,1,s1) // {r4,r6,i4,i6} + vmrglw \b3,\b0,\b1 // vcprm(2,s2,3,s3) // {r5,r7,i5,i7} + vperm \a2,\a0,\a1,v20 // FFT4 ... + vperm \a3,\a0,\a1,v21 + vaddfp \b0,\b2,\b3 // {t1,t3,t2,t4} + vsubfp \b1,\b2,\b3 // {r5,r7,i5,i7} + vperm \b4,\b1,\b1,v25 // vcprm(2,3,0,1) // {i5,i7,r5,r7} + vaddfp \a0,\a2,\a3 + vsubfp \a1,\a2,\a3 + vmaddfp \b1,\b1,v17,v14 // * {-1,1,1,-1}/sqrt(2) + vmaddfp \b1,\b4,v18,\b1 // * { 1,1,1,1 }/sqrt(2) // {t8,ta,t7,t9} + vmrghw \a2,\a0,\a1 + vperm \a3,\a0,\a1,v22 + vperm \b2,\b0,\b1,v26 // vcprm(1,2,s3,s0) // {t3,t2,t9,t8} + vperm \b3,\b0,\b1,v27 // vcprm(0,3,s2,s1) // {t1,t4,t7,ta} + vaddfp \a0,\a2,\a3 + vsubfp \a1,\a2,\a3 + vaddfp \b0,\b2,\b3 // {t1,t2,t9,ta} + vsubfp \b1,\b2,\b3 // {t6,t5,tc,tb} + vperm \a2,\a0,\a1,v23 + vperm \a3,\a0,\a1,v24 + vperm \b2,\b0,\b1,v28 // vcprm(0,2,s1,s3) // {t1,t9,t5,tb} + vperm \b3,\b0,\b1,v29 // vcprm(1,3,s0,s2) // {t2,ta,t6,tc} + vsubfp \b0,\a2,\b2 // {r4,r5,r6,r7} + vsubfp \b1,\a3,\b3 // {i4,i5,i6,i7} + vaddfp \a0,\a2,\b2 // {r0,r1,r2,r3} + vaddfp \a1,\a3,\b3 // {i0,i1,i2,i3} +.endm + +.macro BF d0,d1,s0,s1 + vsubfp \d1,\s0,\s1 + vaddfp \d0,\s0,\s1 +.endm + +fft4_altivec: + lvx v0, 0,r3 + lvx v1,r9,r3 + FFT4 v0,v1,v2,v3 + stvx v2, 0,r3 + stvx v3,r9,r3 + blr + +fft8_altivec: + addi r4,r3,32 + lvx v0, 0,r3 + lvx v1,r9,r3 + lvx v2, 0,r4 + lvx v3,r9,r4 + FFT8 v0,v1,v2,v3,v4,v5,v6,v7,v8 + stvx v0, 0,r3 + stvx v1,r9,r3 + stvx v2, 0,r4 + stvx v3,r9,r4 + blr + +fft16_altivec: + addi r5,r3,64 + addi r6,r3,96 + addi r4,r3,32 + lvx v0, 0,r5 + lvx v1,r9,r5 + lvx v2, 0,r6 + lvx v3,r9,r6 + FFT4x2 v0,v1,v2,v3,v4,v5,v6,v7 + lvx v0, 0,r3 + lvx v1,r9,r3 + lvx v2, 0,r4 + lvx v3,r9,r4 + FFT8 v0,v1,v2,v3,v8,v9,v10,v11,v12 + vmaddfp v8,v4,v15,v14 // r2*wre + vmaddfp v9,v5,v15,v14 // i2*wre + vmaddfp v10,v6,v15,v14 // r3*wre + vmaddfp v11,v7,v15,v14 // i3*wre + vmaddfp v8,v5,v16,v8 // i2*wim + vnmsubfp v9,v4,v16,v9 // r2*wim + vnmsubfp v10,v7,v16,v10 // i3*wim + vmaddfp v11,v6,v16,v11 // r3*wim + BF v10,v12,v10,v8 + BF v11,v13,v9,v11 + BF v0,v4,v0,v10 + BF v3,v7,v3,v12 + stvx v0, 0,r3 + stvx v4, 0,r5 + stvx v3,r9,r4 + stvx v7,r9,r6 + BF v1,v5,v1,v11 + BF v2,v6,v2,v13 + stvx v1,r9,r3 + stvx v5,r9,r5 + stvx v2, 0,r4 + stvx v6, 0,r6 + blr + +// void pass(float *z, float *wre, int n) +.macro PASS interleave, suffix +fft_pass\suffix\()_altivec: + mtctr r5 + slwi r0,r5,4 + slwi r7,r5,6 // o2 + slwi r5,r5,5 // o1 + add r10,r5,r7 // o3 + add r0,r4,r0 // wim + addi r6,r5,16 // o1+16 + addi r8,r7,16 // o2+16 + addi r11,r10,16 // o3+16 +1: + lvx v8, 0,r4 // wre + lvx v10, 0,r0 // wim + sub r0,r0,r9 + lvx v9, 0,r0 + vperm v9,v9,v10,v19 // vcprm(s0,3,2,1) => wim[0 .. -3] + lvx v4,r3,r7 // r2 = z[o2] + lvx v5,r3,r8 // i2 = z[o2+16] + lvx v6,r3,r10 // r3 = z[o3] + lvx v7,r3,r11 // i3 = z[o3+16] + vmaddfp v10,v4,v8,v14 // r2*wre + vmaddfp v11,v5,v8,v14 // i2*wre + vmaddfp v12,v6,v8,v14 // r3*wre + vmaddfp v13,v7,v8,v14 // i3*wre + lvx v0, 0,r3 // r0 = z[0] + lvx v3,r3,r6 // i1 = z[o1+16] + vmaddfp v10,v5,v9,v10 // i2*wim + vnmsubfp v11,v4,v9,v11 // r2*wim + vnmsubfp v12,v7,v9,v12 // i3*wim + vmaddfp v13,v6,v9,v13 // r3*wim + lvx v1,r3,r9 // i0 = z[16] + lvx v2,r3,r5 // r1 = z[o1] + BF v12,v8,v12,v10 + BF v13,v9,v11,v13 + BF v0,v4,v0,v12 + BF v3,v7,v3,v8 +.if !\interleave + stvx v0, 0,r3 + stvx v4,r3,r7 + stvx v3,r3,r6 + stvx v7,r3,r11 +.endif + BF v1,v5,v1,v13 + BF v2,v6,v2,v9 +.if !\interleave + stvx v1,r3,r9 + stvx v2,r3,r5 + stvx v5,r3,r8 + stvx v6,r3,r10 +.else + vmrghw v8,v0,v1 + vmrglw v9,v0,v1 + stvx v8, 0,r3 + stvx v9,r3,r9 + vmrghw v8,v2,v3 + vmrglw v9,v2,v3 + stvx v8,r3,r5 + stvx v9,r3,r6 + vmrghw v8,v4,v5 + vmrglw v9,v4,v5 + stvx v8,r3,r7 + stvx v9,r3,r8 + vmrghw v8,v6,v7 + vmrglw v9,v6,v7 + stvx v8,r3,r10 + stvx v9,r3,r11 +.endif + addi r3,r3,32 + addi r4,r4,16 + bdnz 1b + sub r3,r3,r5 + blr +.endm + +.macro DECL_FFT suffix, bits, n, n2, n4 +fft\n\suffix\()_altivec: + mflr r0 + STORE_PTR r0,r1,\bits-5 + bl fft\n2\()_altivec + addi2 r3,\n*4 + bl fft\n4\()_altivec + addi2 r3,\n*2 + bl fft\n4\()_altivec + addi2 r3,\n*-6 + LOAD_PTR r0,r1,\bits-5 + LOAD_PTR r4,r12,\bits + mtlr r0 + li r5,\n/16 + b fft_pass\suffix\()_altivec +.endm + +.macro DECL_FFTS interleave, suffix + .text + PASS \interleave, \suffix + DECL_FFT \suffix, 5, 32, 16, 8 + DECL_FFT \suffix, 6, 64, 32, 16 + DECL_FFT \suffix, 7, 128, 64, 32 + DECL_FFT \suffix, 8, 256, 128, 64 + DECL_FFT \suffix, 9, 512, 256, 128 + DECL_FFT \suffix,10, 1024, 512, 256 + DECL_FFT \suffix,11, 2048, 1024, 512 + DECL_FFT \suffix,12, 4096, 2048, 1024 + DECL_FFT \suffix,13, 8192, 4096, 2048 + DECL_FFT \suffix,14,16384, 8192, 4096 + DECL_FFT \suffix,15,32768,16384, 8192 + DECL_FFT \suffix,16,65536,32768,16384 + + .rodata + .global EXTERN_ASM\()ff_fft_dispatch\suffix\()_altivec +EXTERN_ASM\()ff_fft_dispatch\suffix\()_altivec: + PTR fft4_altivec + PTR fft8_altivec + PTR fft16_altivec + PTR fft32\suffix\()_altivec + PTR fft64\suffix\()_altivec + PTR fft128\suffix\()_altivec + PTR fft256\suffix\()_altivec + PTR fft512\suffix\()_altivec + PTR fft1024\suffix\()_altivec + PTR fft2048\suffix\()_altivec + PTR fft4096\suffix\()_altivec + PTR fft8192\suffix\()_altivec + PTR fft16384\suffix\()_altivec + PTR fft32768\suffix\()_altivec + PTR fft65536\suffix\()_altivec +.endm + +DECL_FFTS 0 +DECL_FFTS 1, _interleave diff --git a/libavcodec/ppc/types_altivec.h b/libavcodec/ppc/types_altivec.h index 2870e83e7a..36b6e1f388 100644 --- a/libavcodec/ppc/types_altivec.h +++ b/libavcodec/ppc/types_altivec.h @@ -30,6 +30,7 @@ #define vec_s16 vector signed short #define vec_u32 vector unsigned int #define vec_s32 vector signed int +#define vec_f vector float /*********************************************************************** * Null vector |